Replicating the behaviour of SketchUp's plugin "Soap Skin Bubble" in Blender
Cloth simulation can work very nicely as a modelling tool in Blender.
Some differences from the Sketchup add-on you refer to:

Blender Cloth is more general, so there are more settings. They can be saved as presets, though, once you've got them sorted out.
The Sketchup add-on assumes the boundary of the shape is pinned. In Blender, you have to pin vertices explicitly. Create a 'Pin' vertex group, allocate it with weight 1,  and declare it pinned in the 'Shape' panel of the Cloth settings. (Name the group whatever you like)



Blender Cloth Pressure (one of the 'Physical Properties' panels)requires a a closed manifold mesh, otherwise it 'leaks' So, as you see, your shape has been extruded downwards, and the bottom face filled. The rim and base can be discarded after applying the Cloth modifier.
I also added a 'Tension' vertex group to control the shape of inflation.. to give the inflated shape a thinner waist:


Unlike the add-on, the Blender simulation runs as an animation. This one stabilized in about 20 frames.